Couette membrane filtration apparatus for separating suspended components in a fluid medium using high shear

ABSTRACT

The present invention provides significant improvements in the design and performance of a specific type of Rotary Membrane Filter (RMF) apparatus which has the capability of separating particles from a fluid having the same and nearly the same density as the particles by utilizing shear to achieve separation, not centrifugal forces. A particular application for the apparatus is in the processing of fluid suspensions in which the suspensions contain fragile particles which are subject to damage due to excessive shear stresses. The prior art describes processing at constant shear rate, whereas the present invention provides the design and optimization of operation of such an apparatus at constant shear stress, which is maintained at a value below that at which significant damage to the fragile particles is encountered. The use of the invention in plasmapheresis (blood separations) is described in detail, it being understood that the teachings of the invention are also directly applicable to other fluids containing fragile particles. The application of the RMF in a continuous flow processing system designed to extract blood plasma from a donor is described, including return of corpuscular components to the donor.

This is a division of application Ser. No. 812,936, filed Dec. 23, 1985,now U.S. Pat. No 4,755,300.

BACKGROUND OF THE INVENTION

The present invention relates to filtration devices, and in particular,couette membrane filtration systems for separating blood plasma fromwhole blood.

In the filtration and separation of fluid suspensions, devices usingcentrifugal effects exclusively, shearing effects in combination withmembrane filtration and a combination of centrifugal and shearing actionhave been utilized. Devices utilizing centrifugal forces for achievingseparation have been used with suspensions containing sedimentingcomponents. Fluid suspensions, in general, have been filtered by meansof membrane filtration devices. A particular type of membrane filtrationdevice, one in which shearing effects are utilized to obtain filtration,is the couette membrane filter. A couette filter is one which is usuallycharacterized by a series of laminar rotating, cylindrical sheets offluid slipping over one another immediately adjacent a rotating surface.However, a couette filter can also include Taylor vortices withoutdetracting from its ability to filter suspensions so long as thevortices are of laminar character.

In the usual configuration, a couette membrane filtration deviceutilizes a stationary cylindrical container and a cylindrical insertrotatably disposed within the container. The insert typically includes asemipermeable membrane wrapped around and supported by the insert. Thestationary container and insert are dimensioned such that a narrow gapis defined between the inner facing surface of the container and theouter facing surface of the membrane. It is into this gap that the fluidsuspension to be filtered is introduced. In this configuration, if therotation speed is high enough, the laminar flow of cylindrical sheets isreplaced by a laminar flow of a slightly different nature, one which ischaracterized by a regular sequence of counter-rotating toroidalvortices, i.e., Taylor vortices located in the gap. Provided therotational velocity of the cylindrical insert is maintained below acertain upper limit, the toroidal vortices retain their individuallylaminar nature and occur as an alternating sequence of counter-rotatingtoroids which are located in the gap and appear regularly over theentire axial length of the rotatable insert. Such Taylor vortex flow isfurther characterized by a laminar fluid boundary layer located adjacentthe membrane which retains a cylindrical shearing effect for a finitedistance extending from the membrane surface radially into the fluid inthe gap.

A dimensionless number, analogous to the Reynolds number, has beendefined to characterize this flow and is referred to s the Taylornumber. The Taylor number is related to the radius and speed of rotationof the insert, the gap thickness, and the viscosity of the fluidsuspension. According to the classical definition of laminar flow,Taylor flow, for a Taylor number below known limits, can be consideredto be laminar, since the fluid particles follow steady streamlines.

In use, the fluid suspension is introduced into the gap between thefacing surfaces and caused to flow along and parallel to the membranesurface. Rotational motion between the insert and container isintroduced by spinning the insert within the cylindrical container. Therelative rotational motion of the two surfaces creates a rotationalshearing action and the Taylor flow referred to above, which flows aresuperimposed on each other. By providing a sufficiently high shear rate,"...the gel layer of congealed solute, or the concentrated polarizationlayer of particles adjacent the membrane is swept away," as described byLopez. The boundary layer is then characterized by a concentrationgradient of suspended material that increases from nominally zeroconcentration at the membrane surface to the actual bulk concentrationvalues of the fluid suspension in the region just beyond the laminarboundary layer.

The creation of an essentially particle-free boundary immediatelyadjacent to the membrane proceeds from a resolution of opposing forces.Hydrodynamic forces, tending to drive particles of any density away fromthe membrane surface, are due to the fluid shearing action. These forceshave the effect of being repulsive relative to either the rotating orstationary surfaces. Filtration drag produces convective forces actingin the opposite direction. Such drag is due to filtrate passing over thesuspended particle, which must be left behind, as filtrate passesthrough the membrane (a particle may be any enclosed viscousdiscontinuity relative to the suspending medium, e.g., a bubble). Bothforces act at right angles to the flow of the fluid suspension. Theshearing repulsive force and the convective drag force exerted on thesuspended particle are distinct from the pressure forces that drive thesuspension along the membrane or the filtrate toward and through themembrane. Where the repulsive shearing force overbalances the convectivedrag forces, the particle-free boundary layer results. If pressure isnow applied to the fluid suspension, a differential pressure, referredto as transmembrane pressure, TMP, exists across the membrane. Thetransmembrane pressure causes the now-separated fluid in the vicinity ofthe membrane to flow through the pores of the semipermeable membrane andonto the surface of the insert. The separated (filtered) fluid is thendriven by pressure to an outlet from the device where it is collected.The balance of the fluid suspension with its now-increased concentrationof suspended material flows within the gap under the influence ofpressure and/or gravity to a second outlet of the unit where it isremoved.

Such a device can be utilized for the separation of red blood cells fromblood plasma in settings such as in blood donor centers. In the typicaloperation of a plasma donor center, the extraction of blood plasma isthe important objective and the plasma is the material which is retainedby the center typically for later use as plasma or for furtherprocessing to extract certain factors from the plasma. The donor's redblood cells, which are collected at the second outlet from thefiltration device, are then reintroduced into the donor's circulationsometimes utilizing an additional saline solution as a suspending mediumto provide the necessary fluidity and restore donor blood volume.

A limiting factor in the efficient operation of membrane filtrationdevices, particularly when used with blood, is the tendency of suchfilters to experience a phenomenon (polarization) wherein the pores ofthe semipermeable membrane become plugged with the red blood cells fromthe blood suspension to the point where the transmembrane flow of plasmais drastically reduced.

One reaction to this phenomenon has been an attempt to increase thepressure exerted on the fluid suspension introduced into the filtrationdevice in an effort to force the plasma through the plugged membrane.Such efforts have been unsuccessful, however, since increases intransmembrane pressure merely cause more red blood cells to plug thepores of the filter increasing the resistance of the coated membrane tothe flow of plasma therethrough.

It has been thought that a rotating filter type of device is theindicated solution to such a problem. In the configuration where theinterior member is arranged to rotate within the hollow container, theunplugging or unfouling of the filter is sought to be accomplished by acombination of centrifugal action which tends to throw the pluggingmatter off of the surface of the rotating inner element where it isswept away by the "shearing" action that is created by the combinationof the flow of fluid in the gap between the two elements and therelative motion of the two elements to each other.

Such an approach is described in U.S. Pat. No. 3,750,885 which is astrainer device having a rotatable cylindrical screen filter. Particlesin the fluid suspension that build up on the screen filter are said tobe removed from the outside of the screen by a combination ofcentrifugal and shear action. The filter apparatus described in the '855patent provides for rotation of the interior screen section such that acentrifugal type of reverse flow can act together with a "shear" effectto dislodge particles from the screen surface. The centrifugal forcesgenerated on the particles produce an outward radial dislodgement of thecollected particles from the screen and removal from the screen. Thisapproach is useful with heavier high density particles, but it has beenshown in the scientific literature that centrifugal effects on nearlyneutrally buoyant particles, such as red blood cells, are completelymasked by shearing effects when the shearing effects are at a level tobe useful for filtration.

Use of shearing effects to specifically obtain filtration of blood isdescribed in U.S. Pat. No. 3,705,100 to Blatt. As described therein, theuse of shearing effects on blood results in an improvement in theefficiency of the flow of plasma through the membrane. This approach hasbeen used in later channel-type devices where an attempt has been madeto achieve large membrane areas having relatively high rates of shear soas to obtain devices which are sufficiently efficient to obtain rates offlow which make the devices suitable for use in clinical settings suchas blood donor centers. However, in the case of blood donor centers, thedonor's natural blood flow rate is usually too low to achievesufficiently high rates of shear and large membrane areassimultaneously.

A solution to this problem is provided in U.S. Pat. No. 4,212,742,wherein the concept of recirculation of the blood through the device isintroduced. However, with or without recirculation, the viscosity ofblood is such that the very high shear rates suggested by Blatt, viz.,in excess of 2000 sec.⁻¹, cannot be achieved unless high drivingpressure is employed as well. Consequently, there exists an unacceptablyhigh TMP and associated polarization described earlier which cannot bemitigated because of the operation of physical principles governing flowunder these conditions. This polarization problem is further compoundedin that the deposition of red blood cells on the membrane causes severedamage to the cells, making the red blood cells unsuitable for return tothe donor.

Others have taken the approach of accepting much lower rates of shearcompensated by a very much increased membrane area, it being understoodthat less shear is accompanied by substantially lower permeate fluxrates per unit of membrane area. This approach works better than thehigh shear method because the additional membrane required bears anon-linear, i.e., power less than one, relationship to the lowering ofshear rate and permits the same total permeate flux for the device as awhole to be achieved with less driving pressure. Nevertheless, themembrane areas required in this case are very large and costly,rendering the device prohibitive for some uses such as donor plasmacollection or large-scale therapeutic apheresis.

Still another consideration that must be taken into account in thedesign of either a couette type filter or channel device is the factthat, as such devices are used with blood, and plasma is extracted asthe whole blood flows through the device, the extraction of plasmaresults in an increasing cell concentration, i.e., hematocrit of theremaining concentrated blood. Not only does viscosity increase rapidlywith increasing hematocrit, but it can also be seen that the tendency ofthe exit portion of the filter to become plugged also increasesmarkedly. Both the increase in viscosity and filter plugging contributeto blood cell damage.

SUMMARY OF THE PRESENT INVENTION

The present invention addresses the foregoing problems by providing anapparatus for filtering fluid suspensions wherein the inventioncomprises an elongated hollow container having an interior wall with afirst predetermined tapering profile. An elongated core element isdisposed within the container. The envelope of the core element has asecond predetermined tapering profile such that a gap having a widthwhich varies in the direction of elongation in a predetermined manner isdefined between the exterior wall and the core element. Inlet means arelocated at one end of the apparatus, and means are provided forintroducing a fluid suspension under pressure through the inlet meansinto the gap. Means are provided for rotating the core element withinthe container at a predetermined angular velocity, such that shearstress, of a value less than a predetermined maximum limit, is imposedon the fluid suspension, the shear stress being essentially constantover the entire longitudinal extent of the core element due to thegeometry and configuration of the gap. Further, the geometry andconfiguration of the gap is such that the rotation produces laminar flowwithin the suspension, possibly of a Taylor vortex character. Firstoutlet means are also located at the inlet end of the apparatus forremoving fluid extracted from the fluid suspension, and second outletmeans are located at the end of the apparatus opposite the inlet end forremoving the remaining portion of the fluid suspension. Membrane meansare disposed over the exterior surface of the core element and/or overthe interior surface of the container for filtering and separating thefluid from the fluid suspension when the core element is rotated, andmeans are provided for communicating the filtered fluid from the side ofthe membrane opposite the fluid suspension to the first outlet means.

In use, a fluid suspension such as whole blood obtained from a plasmadonor is pumped into the apparatus. The fluid suspension flows underpressure into the gap between the hollow container and the core elementand fills the entire generally annular space (gap) from the inlet to theoutlet end of the apparatus. The concentric core element is rotated at aselected angular velocity for the gap dimension being utilized, whichproduces a Taylor number for the apparatus corresponding to the laminarflow of the fluid suspension and below the Taylor number at which randomturbulence is produced.

The shearing action produces a laminar boundary layer immediatelyadjacent the membrane that consists essentially of the suspending fluid(plasma) only. The suspended material (red blood cells) is repelledtoward the center of the gap and, as a result, the plasma is induced,under the influence of the pressure exerted on the fluid suspension, toflow through the pores of the membrane and onto the surface of the coreelement and/or interior wall of the containment vessel. The flow ofplasma through pores in the membrane takes place over the entire surfaceof the membrane, and it can be seen that, as the whole blood movesthrough the apparatus from inlet to outlet, the amount of plasma presentis diminishing and therefore the hematocrit increases as does theviscosity of the remaining whole blood on the upstream side of themembrane.

In qualitative terms, the radius of the rotating core element varieswith the radius of the interior wall so that the gap thickness increasesin a predetermined manner from blood inlet (normally located at the topof the device oriented with its spin axis vertical) to blood outlet atthe bottom of the filtration unit to accommodate the increasinghematocrit and viscosity. In general, the gap is smaller near the top(or blood inlet) and wider at the bottom near the outlet for the redblood cells and, in one specific embodiment, the profile of the interiorwall of the container and the exterior membrane surface of the rotatingelement are sections of inverted truncated cones. The specificdimensions of the gap at each interval along its longitudinal extent ischosen so as to maintain a constant shear stress on the .fluidsuspension that is located in the gap, even as that fluid suspensionchanges its viscosity along the longitudinal extent.

It has been shown in the scientific literature that red blood celldamage respecting the flow of blood in the vicinity of foreign surfacesis uniquely related to shear stress. Above a certain limit of shearstress, serious damage to the red blood cells occurs. Below that limit,virtually no damage is encountered. In the present invention, othersources of hemolysis are minimal.

Particularly applicable to the present invention is the work of Nevarilwho studied hemolysis at very high rates of shear in a couetteviscometer, essentially equivalent to the couette membrane filter forpurposes of the question at hand. Nevaril discovered that, below a shearstress value of 1500 dynes/cm², hemolysis, either immediate or latent,was too low to be detected in his apparatus. Between shear stress valuesof 1500 and 3000 dynes/cm², there began to occur a rapidly increasingrate of morphological change in the RBC which resulted in removal ofthese damaged RBC from the circulation within 24 hours of reinfusioninto the donor. This is indicative of latent cell damage and may beconsidered to be equivalent to outright cell destruction for clinicalpurposes. Above 3000 dynes/cm², cell destruction was immediate andcomplete. Clearly, for purposes of device design regarding the presentinvention, 1500 dynes/cm² should be taken as a safe upper limit.

It is the essence of the present invention that this particularstructure and this particular geometry results in a constant shearstress on the fluid of a value just below the limit at which RBC damageoccurs and that this geometry and structure compensates for the changein viscosity due to changing hematocrit as plasma is withdrawn resultingin highly efficient plasma collection, while minimizing damage to thered blood cells of the donor which are normally reinfused into the donorafter the plasma extraction has been accomplished.

The solution provided by the present invention proceeds from the work ofLopez as described in Ultrafiltration in Rotary Annular Flow (Ph.D.Dissertation, University of Lund, Sweden, 1979) and in "Ultrafiltrationat Low Degrees of Concentration Polarization: Technical Possibilities,"Desalination, Vol. 35, pp. 115-128, 1980, and in his Swedish Patent No.7711142-5 dated Oct. 5, 1977, where he describes the use of a couettemembrane filter capable of producing arbitrary rates of shear withoutregard to flow rate or resistance through the device which is theproblem that plagues channel type devices. Lopez demonstrated that shearin a couette membrane filtration device is achieved independently of theflow rate through the device.

Adapting the Lopez teaching to the filtration of blood in the presentinvention results in the provision of a couette membrane filtrationdevice utilizing a stationary outer wall and a rotating inner membrane.Because centrifugal forces are ineffectual in a couette membranefiltration device used with blood, an equivalent configuration notdisclosed by Lopez or found in the prior art places the membrane on theinterior surface of the containment vessel. In either case, the presentinvention prefers rotation of the inner surface to produce the shearingaction. The use of a rotating inner surface, whether or not that surfacecarries a membrane, adds an additional practical advantage in that itmeans that the inlets and outlets from the device can be located in thestationary outer container, thereby eliminating external rotating seals.Such external seals, when required, result in a myriad of problems,including susceptibility to septic contamination and leakage.

The operating parameters include operation of the device with a selectedshear rate that will prevent polarization (plugging) of the membrane forthe amount of plasma to be obtained in each cycle of operation, whilestill achieving the filtration efficiency required. Greatest efficiencyresults from devices using the narrowest possible gaps and lowest speedsof rotation that still achieve the desired shear rate. By keeping thegap small, thus resulting in low total blood volume in the device at anygiven interval, the residence time of blood in the device is minimized.This factor, combined with operation at a shear rate which avoidspolarization of the membrane, minimizes damage to the red blood cells,i.e., prevents or minimizes hemolysis, bearing in mind that the maximumusable shear rate at any point within the gap is limited by the shearstress limit as described above.

In the presently preferred embodiment, the filtration unit according tothe present invention consists of a hollow container having theconfiguration of a generally tapering surface of revolution and amembrane-covered core element or spinner having a configuration thatgenerally follows the configuration of the hollow container. A solidmounting pin is integrally molded into one end of the spinner andlongitudinally extending channels are molded into the exterior surfaceof the spinner. A spinner cap is mounted at the end of the spinner, anda hollow pin disposed about the axis of the cap is integrally moldedwith the cap. The general profile of the inner facing wall of thecontainer and the outer facing surface of the spinner are that ofelongated inverted truncated cones. The spinner is dimensioned so as toprovide a small annular gap between the inner and outer facing walls. Ingeneral, the filtration unit is oriented with is spin axis vertical andfirst inlet means at the top. In this orientation, the dimension of thegap increases from top to bottom of the unit. The hollow pin molded intothe top of the spinner cap communicates with the interior of thefiltration apparatus of the present invention. An end cap having ahollow passage in the top thereof for receiving the hollow pin on thespinner cap in a radial bearing relationship is mounted on top of theassembly and is secured to the periphery of the hollow container. Aportion of the exterior surface of the hollow pin also serves as asealing surface more specifically described, hereinafter. All parts ofthe filtration device are adapted to be injection-molded from materialssuch as polycarbonate and, in keeping with present practice, the entireunit is intended to be disposable after use with one specific donor.

An inlet port enters through the top of the end cap and is located at anangle to the hollow pin. The inlet port is directed at the spin axis ofthe hollow pin so that blood entering the unit can flow into the top ofthe unit against the spinning hollow pin and along the pin onto the topof the spinner cap and thence into the gap.

This configuration causes blood to flow into the unit symmetricallyagainst the slowest velocity surface with minimum trauma and nostagnation points. The admitted whole blood proceeds over the top of theend cap and down the sides of the inner wall of the container throughthe gap. As discussed above, in the transit of the whole blood throughthe gap, plasma is separated from the whole blood in a laminar boundarylayer adjacent the membrane due to the shearing action produced by therotating spinner and, under the influence of transmembrane pressure,passes through the pores of the semi-permeable membrane into thechannels where it flows up through the channels into the spinner capmanifold and thence through the hollow pin to an outlet at the top ofthe unit. The remaining concentrated red blood cells pass through to thebottom of the unit and outwardly through exit ports.

Rotational drive for the spinner unit is accomplished by magneticcoupling between a drive source located externally of the apparatus anda magnet mounted in the interior of the spinner unit.

In the presently preferred embodiment, the magnet in the spinner unit isa piece of radially oriented four-pole ceramic magnet. The spinner andmagnet combination then serves as an armature which is magneticallycoupled to magnets disposed in a holder which positions fourcorresponding radial magnetic poles around the exterior of thecontainer. A synchronous motor can be used to drive the holder, and themagnetic coupling with the interior magnet produces rotation of thespinner at the desired angular velocity.

Since the spinner is hollow and is designed so that it is light inweight, it is neutrally buoyant or nearly so in whole blood and floatsin the whole blood which is supplied to the unit. The light weight andfloatation of the spinner unit reduces the criticality of the magneticcoupling. A further advantage is derived in that, with the magnetencased within the spinner unit, it is totally sealed from the blood andplasma and no possibility of contamination exists from this direction.

A shallow spiral groove is imparted to the exterior surface of thehollow pin. The direction of the spiral groove is chosen so that aslight pumping action, opposite to the direction of plasma outflow, isestablished. For example, when the magnetic coupling to the unit isarranged so as to drive the spinner in a right-hand direction, aright-handed spiral groove is imparted to the pin. If rotation isleft-handed, a left-handed spiral groove is used. The spiral groove isdesigned so as to have the effect of exerting a slight pumping actionwhich causes a small amount of plasma exiting from the outlet port to bepumped back into the unit and to exert a small pressure on whole bloodadmitted to the interior of the filtration unit, greatly enhancing theeffectiveness of the seal around the hollow pin and preventing wholeblood, i.e., red blood cells, from leaking through the top of the unitinto the filtered plasma.

The configuration of the present unit also means that plasma is removedfrom the top of the unit and thus keeps the seal at the plasma outlet ata point which is remote from the heaviest concentration of red bloodcells.

DESCRIPTION OF THE DRAWINGS

These and other aspects of the present invention will be betterunderstood by reference to the drawings, wherein:

FIG. 1 is a sectional view in elevation of a filtration separationapparatus according to the present invention.

FIG. 2 is a sectional view in elevation, partially broken away, of theapparatus of FIG. 1.

FIG. 3 is a top plan view of a spinner element used in the apparatus.

FIG. 4 is an elevation view of the spinner element.

FIG. 5 is a sectional view of the spinner element taken along lines 5--5of FIG. 3.

FIG. 6 is a top plan view of a cap for the spinner element including amanifold.

FIG. 7 is an elevation view of the spinner cap.

FIG. 8 is a top plan view of the assembled filtration apparatusaccording to the present invention.

FIG. 9 is a plan view of an annular piece of membrane material showing asection thereof ready for attachment to the spinner element.

FIG. 10 is a perspective view of the spinner element and cap with asemi-permeable membrane secured to the exterior surface.

FIG. 11 is a schematic diagram of a plasmapheresis system using amembrane filtration apparatus according to the present invention.

FIG. 12 is an enlarged vertical sectional view of a portion of thefiltration separation apparatus according to the invention showing theaxial flow of the fluid suspension in the gap and the Taylor vorticeswhich are formed.

FIG. 13 is a view taken along lines 13--13 of FIG. 12 showing theboundary layer regions adjacent the facing surfaces of the filtrationseparation apparatus and the gradation of suspension concentration.

FIG. 14 is a sectional view in elevation of an alternate embodiment ofthe apparatus according to the present invention.

FIG. 15 is a graph plotting the variation of critical filtrationvelocity with hematocrit for two mathematical models of filtrationapparatus.

FIG. 16 is a graph plotting expected hemolysis vs. shear stressillustrating the improvement obtained by the present invention incomparison to the prior art;

FIG. 17 is a schematic diagram illustrating the gap dimension betweenthe membrane and the stationary wall of the containment device accordingto the present invention;

FIG. 18 is a graph illustrating the relationship of Taylor numbers andangular velocity of the spinner as a function of the initial gap spacingof the membrane and stationary wall;

FIG. 19 is a graph depicting the mean filtration velocity of the presentinvention as a function of plasma fraction extracted for several valuesof shear stress τ_(M) ;

FIG. 20 is a graph illustrating the improvement in the figure of meritof the present invention relative to the prior art (Lopez) as a functionof the plasma fraction extracted.

FIG. 21 is a graph depicting the variation of hematocrit with thenormalized length of the spinner for several values of plasma extractionfraction;

FIGS. 22A and 22B are graphical illustrations of the qualitativevariation of gap spacing as a function of normalized length of thespinner for plasma extraction fractions of 0.8 and 0.9 respectively;

FIG. 23 is a graph showing a design parameter of the device according tothe present invention as a function of plasma fraction for severalvalues of H₁ ;

FIGS. 24A and 24B are graphs similar to FIGS. 22A and 22B for theconical spinner configuration.

FIG. 25 is a graph plotting the normalized Taylor number of the deviceas a function of normalized length; and

FIG. 26 is a graph depicting the critical filtration velocity as afunction of normalized length for several values of plasma extractionfraction.

DETAILED DESCRIPTION OF THE INVENTION

A membrane filtration apparatus 10 according to the present invention isshown in FIG. 1. This apparatus is specifically intended for use inseparating plasma from whole blood, for collecting the plasma andconcentrated red blood cells after the separation has been accomplished,and for returning red blood cells to the donor after the plasmacollection has been completed. As shown therein, the apparatus consistsof a stationery elongated containment vessel 12 and an elongatedrotatable spinner 14 disposed within vessel 12. The interior wall ofvessel 12 has a tapering profile from top to bottom, and spinner 14likewise has a tapering configuration which generally follows theinterior taper of the vessel. As seen in FIGS. 1 and 2, the outersurface of spinner 14 is invested with a plurality of longitudinalchannels 17 in the exterior surface of the spinner forming ribs 16therebetween.

A porous semipermeable membrane 18 extends around and overlies theexterior surface of the spinner 14. The interior wall 20 of thecontainment vessel 12 is slightly concave inward in longitudinal profilegiving said interior wall 20 an inverted approximately conical axialcross-section such that the spacing of inwardly facing wall 20 along itsentire longitudinal extent from the straight outer surfaces as seen inlongitudinal axial section, of the longitudinal ribs is maintained at adistance determined according to the principles of the present inventionso as to define a narrow gap 21 between the interior wall of the vesseland the semi-permeable membrane which is wrapped around the spinnermember. The thickness of the gap varies in the longitudinal directionand is maintained at a width at each point such that the shear stress towhich the blood is subjected during the plasma extraction interval ismaintained at an essentially constant value less than 1500 dynes/cm²over the entire length of the membrane surface in spite of the largeincrease in blood viscosity as the blood transits the length of theapparatus. Spinner 14 is rotatably mounted by means of pin 22 extendingthrough aperture 24, which is molded into the base of the containmentvessel.

A spinner cap 26 is located at the top of spinner 14 and is force-fittedand secured in an opening at the top of a cavity 39 in the interior ofspinner 14. A four radial pole ceramic disk magnet 28 is mounted incavity 39 below cap 26. Magnet 28 is bonded to the interior wall of thespinner. By means of a drive mechanism 29 magnetically coupled to magnet28, spinner 14 is caused to rotate on its axis of rotation when theplasma separation apparatus 10 according to the present invention isoperated. A series of conduits 30 functioning as a manifold extend fromthe recessed perimeter 37 of spinner cap 26 to its axis. The recessedperimeter 37 of spinner cap 26 forms a circumferential collectionchannel 89 at the ends of the channels 17 in spinner 14.

Conduits 30 communicate with and extend from the circumferentialcollection channel 89 formed between spinner 14 and cap 26 to anupwardly directed passage 34 in hollow pin 32, which, in the presentlypreferred embodiment, is integrally molded with cap 26. Containmentvessel 12 is sealed by means of a cap 38 which defines an inlet port 40where whole blood is introduced into the apparatus and an elongated,hollow conduit 36 which provides a radial bearing surface for pin 32which is adapted to be slidably fitted therein. Conduit 36 is a firstoutlet port from the apparatus of the present invention for plasmaextracted from blood admitted to the apparatus. Outlet ports 42 at thebottom of the unit serve as second outlet ports for removal of theconcentrated red blood cells remaining after the plasma has beenfiltered out.

Inlet port 40 is also located in the top of cap 38 disposed at an anglewith respect to the axis of the apparatus and is directed at thecenterline of the upwardly directed hollow pin 32. Blood entering theapparatus flows into port 40 and against and along pin 32. Port 40 isutilized both as an inlet for the introduction of fluid suspensions suchas whole blood into the device and an outlet for concentrated red bloodcells suspended in remaining plasma and possibly additional isotonicsaline solution when the device is operated with flow reversed.

The spinner element is shown in further detail in FIGS. 2, 3, and 4.FIG. 3 is a top plan view of the spinner element 14 showing its exteriorsurface 15, into which ribs 16 and channels 17 are molded. The narrowingtaper of the channels 17 from the top to the bottom of the spinnerelement can be seen in each of these figures. The depths of thesechannels also diminishes over the longitudinal extent of the spinnerelement from top to bottom thereof. One rib 52 is wider than the rest ofthe ribs 16 on the exterior surface of the spinner, and provides a landor base to which the membrane is secured as will be discussed in moredetail in conjunction with FIG. 9.

As can be seen in FIGS. 2 and 5, the interior of the spinner element ishollow and has a stepped configuration which provides a shoulder 25located in cavity 67 of the hollow spinner element. Shoulder 25 providesa shelf on which ceramic magnet 28 is seated. The bottom 27 of theinterior of the spinner element is spaced approximately twice as farfrom shoulder 25 as the top surface 13 of the spinner element. Mountingpin 22 provides the axis about which the spinner element rotates.

As shown in FIG. 1, pin 22 is molded as an integral part of the spinnerelement. The exterior surface at the bottom of the spinner element isgenerally trapezoidal in axial cross-section, as is best seen in FIG. 5.The perimeter of the bottom exterior surface of the spinner element isshown at 87 in FIGS. 2, 4, and 5. The exterior surface of the bottom ofthe spinner element corresponds to the contour of the interior surfaceof the bottom of container vessel 12.

The cap for spinner element 14 is shown in plan view in FIG. 8 and inelevation view in FIG. 7. The cap comprises a plug portion 35 at itsbase having a first diameter, an intermediate circular portion 37defining a shoulder 48 and a top portion 39 having a diameter greaterthan the diameter of intermediate portion 37 and defining a secondshoulder 49. As shown therein, three ports 30 extend from the perimeterof intermediate portion 37 into the center interior of element 14, asbest seen in FIG. 6. Ports 30 communicate with passage 34 in hollow pin32. As shown in FIG. 7, a shallow spiral groove 83 is imparted to theexterior surface of pin 32. Spinner 14 is arranged to rotate in aleft-hand direction, groove 83 is left-handed, as shown. The grooveexerts a pumping action on plasma emerging from passage 34. A minuteamount of plasma is carried by groove 83 along the interior of sleeve 36into the space above cap 26, thereby exerting a slight amount ofpressure on the blood in said space, preventing its migration upwardlyalong the interior of sleeve 36.

When the unit is assembled, spinner cap 26 is mounted on top of spinnerelement 14. Plug 35 is adapted to fit tightly within the opening at thetop of spinner element 14 with shoulder 48 seated on top surface 13.Ports 30 are molded at an angle through intermediate portion 37 andcommunicate with conduit 34 in pin 32.

The end cap 38 for the filtration unit according to the presentinvention is shown in plan view in FIG. 6. A hollow sleeve 36 is formedin the top of the cap for receiving hollow pin 32. When the unit is inoperation, plasma passes through the pores of the membrane and flowsupwardly along channels 17 to top surface 13 where it is collected inchannel 89 flowing further into ports 30 and further upwardly to conduit34. The plasma then flows through conduit 36 into tubing (not shown)which is connected to the outlet port.

The perspective view shown in FIG. 10 shows the manner in which asemi-permeable membrane 18 is mounted on spinner 14. Membrane 18 is cutto size and wrapped around the exterior surface of spinner element 14 sothat the ends 54 of the membrane are brought together in abutment and inposition so as to overlie rib 52. The portions of the membrane whichoverlie the exterior surface of rib 52 are bonded to that surface. Theremainder of the ribs 16 serve as a support structure for the membrane.In addition, spinner cap 26 is seated on top of the spinner element sothat a shoulder 50 extending downwardly from surface 48 of cap 26 mateswith and abuts with the top of rib 52. Membrane 18 is of an overalllongitudinal length so that when secured to the spinner element, a firstend of the membrane completely overlies channel 89 between cap 26 andspinner 14 and is also bonded to the exterior surface 56 of shoulder 50and the exterior surface of top portion 39. Membrane 18 overlies theentire longitudinal surface of spinner 14 extending below the ends ofthe longitudinally extending ribs 16 and channels 17 and terminating atcircular edge 87 adjacent the base of the spinner. When spinner element14 is rotated, plasma separated from the blood flowing downwardly in thegap 21 passes through the pores of the membrane and then flowsinteriorly of the membrane upwardly in channels 17 into channel orheader space 89 beneath surface 49 around the periphery of cap 26 toconduits 30 of the manifold.

In one embodiment, membrane 18 is obtained by cutting a sector out of anannular piece of flat membrane material, as is shown in FIG. 9. In FIG.9, an annulus 60 of membrane material is depicted. Because the profileof the spinner element 14 is that of a truncated cone, a suitable pieceof membrane material can be prepared by cutting a sector from theannulus along radii defining a predetermined angle 92 at the center ofthe annulus and then wrapping this piece of membrane around the spinnerelement. In the presently preferred embodiment of the invention, this isthe procedure used to obtain membrane sheet 18. It is also possible toprovide the membrane by casting membrane material on a suitably shapedmandrel and thereafter removing it and placing it on the spinner orcasting the membrane directly on a suitably prepared spinner surface.There are a wide variety of commercially available sheet membranes in aplurality of materials and porosities. A particular material having aparticular porosity is selected for its suitability with respect to thespecific fluid suspension which is to be filtered by the apparatus.

In the case of whole blood, a material such as polycarbonate membranematerial having 0.6 micron pores and a thickness of 10 microns isutilized in the presently preferred embodiment of the invention.

The enlarged fragmentary views in FIGS. 12 and 13 illustrate the natureof the flow patterns of the fluid suspension as it proceeds axiallyalong the gap of the filtration apparatus according to the presentinvention. In FIG. 12, a longitudinal section of the apparatus, theaxial flow 90 of the bulk fluid suspension, is shown in gap 21. Membrane18 is shown disposed on spinner element 14 facing the interior wall 20of the containment vessel 12. A series of alternating Taylor vortices91a, 91b are formed in the gap as spinner element 14 is rotated at itspredetermined angular velocity. As indicated above, the Taylor vorticesare in the form of a series of toroids around the spinner extendingaxially through the apparatus and the view of the vortices shown in FIG.12 is a section through four such toroids. These toroidal vortices arealso laminar in character and rotate at right angles to the direction ofrotation of the spinner. A laminar boundary layer 93 is formed betweenthe vortices and the facing surfaces of the spinner element and interiorwall of the vessel which, due to the combination of laminar shearingactions, is essentially cell-free immediately adjacent the surface ofthe membrane. Thus, in operation, there are three flows operatingsimultaneously on the fluid suspension: the basic shearing action of thespinning membrane, the Taylor vortex flow, and the axial flow of thesuspension through the apparatus.

In FIG. 13, a plan view taken along lines 13--13 of FIG. 12 (a sectiontaken between Taylor vortices), the cell concentration gradient 95 canbe seen in gap 21, as well as the cell-free boundary layers 93. The ribs16 and channels 17 on the surface of spinner element 14 are seen in FIG.13 and support membrane 18. Where the present apparatus is used tofilter plasma from whole blood, plasma first flows through the pores 84of membrane 18 into channels 17 under the influence of the transmembranepressure and then proceeds axially through channels 17 to the collectionpoint.

An alternative embodiment of the filtration separation apparatusaccording to the present invention is shown in FIG. 14. Here themembrane is attached to the interior wall of the containment vessel andthe spinner element is provided with a smooth surface.

In this embodiment the apparatus comprises a containment vessel 96having a specially configured interiorly facing surface 97. Surface 97has a plurality of channels 98 molded into it which define a pluralityof ribs 99 extending around the inner circumference of the containmentvessel. A semipermeable membrane 100 is bonded to or cast upon ribs 99to provide the filtration medium for the apparatus.

A spinner element 101 is rotatably mounted by means of mounting pins102, 103 at opposite ends of the interior of vessel 96 and is providedwith a smooth uncovered surface. A fluid suspension such as whole bloodis introduced into the apparatus through inlet port 104 and flowsdownwardly through gap 105 between spinner element 101 and membrane 100toward outlet 106. As before, the gap is maintained in the configurationthat it is at its narrowest or minimum dimension at the point where theincoming blood enters gap 105 and increases in width in the axialdirection toward the outlet to its widest dimension at the base ofmembrane 100. As the whole blood moves axially through the apparatus,the spinner is rotated at a predetermined angular velocity such thatshear stress is maintained below a predetermined maximum. Plasma isseparated from the whole blood in the shear flow and passes under theinfluence of the transmembrane pressure through the pores of membrane100 into channels 98 and thence upwardly to collection channel 107 andfinally to fluid outlet port 108. Thus, in this embodiment, the membraneis mounted on the stationary surface as opposed to the rotating surfacein the embodiment of FIG. 1. The present invention also includes aconfiguration in which a membrane is mounted on both the rotating andstationary surfaces. In this embodiment, collection channels for thefluid passing through the membranes are provided for each membranecovered surface.

A block diagram shown in FIG. 11 illustrates a type of plasmapheresissystem in which the filtration unit according to the present inventionis utilized. It should be understood that the diagram is schematic andillustrative only and not specifically indicative of the manner in whichthe filtration apparatus of the present invention is used. As showntherein, a filtration unit 70 according to the present invention, hasits inlet port 71 connected to a first pump means 61 by means of alength of tubing 72 which also connects pump 61 to a suction control 73and by another length of tubing 74 to a hypodermic needle 75. Thehypodermic needle 75 is utilized to connect the system to the plasmadonor. A first outlet port 76 is connected to a second pump 63 by meansof tubing 77 which also connects pump 63 to a plasma collection bottle78. A second outlet port 80 at the bottom of unit 70 is connected bymeans of tubing 81 to a red blood cell collection bag 82. Bag 82 has anoutlet port 83 which is, in turn, connected by tubing 84 through asolenoid clamp 65 to a cannula 85 which is adapted to be connected to asupply of anti-coagulant or saline (not shown).

In the plasma-collection phase, air is first cleared from the system bymeans of reverse pumping of anti-coagulant from cannula 85 to hypodermicneedle 75 by means of peristaltic roller pump 61, after first openingsolenoid clamp 65 to admit a predetermined amount of anticoagulant orsaline to bag 82. Rotation of the filtration unit 70 is then started,the hypodermic needle 75 is connected to the donor, the system is primedwith blood across suction control 73, which is provided to protect thedonor from excessive suction, and blood is pumped into unit 70. Whenunit 70 is filled with blood from the donor, a second pump 63 is turnedon to withdraw plasma from outlet port 76. In the usual case, five tosix hundred milliliters of whole blood are withdrawn from the donor, andthe filtration unit separates the whole blood admitted into the nit intoplasma which is conducted out of the port 76 to the plasma-collectionbottle 78 while packed red blood cells are communicated through thesecond outlet port 80 to the packed red blood cell collection bag 82.

Thereafter, plasma pumping ceases and the red blood cells which arestored in collection bag 82 along with added saline, as required, arereinfused into the donor by reverse pumping through unit 70 using bloodpump 61 pumping in reverse. Cannula 85 may be connected to a source ofsaline and/or anti-coagulant (not shown) which may be admitted into bag82 upon opening of solenoid clamp 65. Either saline solution oranti-coagulant in metered amounts is introduced as a suspending mediumfor the red blood cells, and the red blood cell suspension is pumpedback through second outlet 80 of the separator unit 70 and thencethrough the inlet port 71 through the tubing connected to the donor backinto the donor. This procedure is repeated a second time after the firstreinfusion has been completed so that donor blood volume is nevercompromised. System operation is discontinued when the collected redblood cells have been completely reinfused into the donor a second time.For a donor having normal bleeding rates of 50 to 60 ml/min., theextraction process utilizing somewhat more than two half-liters of wholeblood and yielding about one half-liter of undiluted protein richplasma, takes approximately 30 minutes.

In order to facilitate the practice of the methods and principles of theinvention as described in the foregoing, it was necessary to expressthese in rigorous quantitative terms that yield specific geometricalconfigurations and operating parameters. This is a discipline that canbe applied by those skilled in analysis. Therefore, the detailedmathematics are not included here. On the other hand, a discussion ofempirical data, design examples and several important assumptions wouldprove useful to those who would practice the invention. The pivotalprinciples which form the foundation of any design in accordance withthe invention may be summarized as follows:

1. A couette membrane filter (after Lopez) is utilized wherein shear isinduced by rotation independent of flow through the device.

2. The induced shear must be laminar (i.e., not turbulent), although theshear profiles are of a Taylor vortex character because a spinning coreelement in a stationary containment vessel is the preferredconfiguration (also in accordance with Lopez).

3. Departing now from Lopez, the invention seeks to optimize the use ofthe couette membrane filter configuration for separating mechanicallysensitive suspensions by causing two things to happen simultaneously.These are:

A. Shear stress, i.e., τ=μS, where μ is local viscosity and S is localshear rate, is required, by reason of design and operating parameters,to be constant over the entire actively filtering membrane surface.Thus, if shear stress is increased or decreased for any reason, e.g. aswith spin rate, it must change uniformly over the entire membrane; and

B. The local rate of filtrate flow through the membrane shall,everywhere, be just less than that which causes "polarization" orfouling of the membrane. This filtrate flow has the dimensions of avelocity and shall be referred to as the critical filtration velocity,U_(c). (Note: ml/cm² -sec is equivalent to cm/sec).

4. A feature which is attributed to many mechanically sensitiveparticles in suspension puts a limit on shear stress which uniquelycharacterizes their tendency to become damaged when subjected to shearflow near walls. This statement is strictly true only if item 3.B. aboveis also in effect. Otherwise, filter plugging is an overriding source ofparticle damage. Consequently, shear stress is allowed to increase, forexample, by increasing the spin rate, only up to a point below thecritical damage limit.

An immediate benefit follows from the above design criteria due to thefact that the critical filtration velocity, U_(c) increasesmonotonically with increasing shear rate, S. If shear stress τ iseverywhere uniform and accordingly, everywhere maximum, then it followsthat S, and therefore U_(c), is also maximized, although varyingdepending upon the local value of viscosity, μ. Maximizing U_(c)everywhere on the membrane and, in accordance with item 3.B. above,passing filtrate at a velocity very near that value, is equivalent tooptimizing the performance of the device.

Furthermore, the fact that shear stress is the dominant source ofparticle damage under the stated operating conditions and is everywhereuniform in value means that the rate of particle damage is uniform overthe entire membrane as well. One then selects the degree of acceptabledamage by selecting spin rate. In effect, U_(c) is everywhere maximumfor the degree of particle damage that is determined to be acceptable.Blood being used as a specific example, it is noted that red bloodcells, RBC, are peculiarly damaged when the shear stress exceeds 1500dynes/cm.² regardless of shear rate.

As with most particle suspensions, fluid viscosity will increase asplasma or filtrate is withdrawn, leaving a thicker suspension behind.This sets up the analytical problem wherein one must compute the localviscosity of the suspension in the face of varying particleconcentrations as a function of axial position from suspension entry tothickened suspension exit under the operating conditions defined above.The solutions are peculiar to the type of suspension being filtered andits particular properties as noted above. Specific solutions will begiven for normal human whole blood. Once the viscosity function isdetermined, one can manipulate geometric parameters, principally theshear gap thickness, to control the corresponding shear function suchthat, μS is a constant and the problem is essentially solved, providedone was also careful to avoid turbulence in the design. Even so, it willbe seen in the discussion to follow that a wide selection of geometriesis available within the principles of the invention. The flexibilitylies mainly in the choice of spinner shape, although certain shapes aremore conducive to stable laminar flow than others.

One central conclusion to be drawn from the analysis is that certainbasic operating parameters, such as plasma extraction rate, on the wholeand specifically as a function of position along the membrane (i.e.,referred to throughout as critical filtration velocity), overallefficiency per unit membrane area, and expected rate of hemolysis (i.e.,blood damage), can all be stated without specific reference to thegeometry of the device, particularly spinner shape and gap thickness. Itis further seen that spin rate is a unique function of the ratio of gapthickness to spinner diameter, that is, referred to a given point in thedevice such as at the blood entry end of the actively filtering portionof the membrane where the gap is usually narrowest. The narrower thegap, the slower one can spin and still reach maximum device efficiency,i.e., at the maximum accepted shear stress level. The choice is apractical trade-off between dynamic stability considerations anddimensional tolerances. The gap shape, that is, the way the gapthickness changes with position along the membrane, will depend upon theselection of spinner shape such that the μS product is a constant overthe entire active portion of the membrane. Finally, the choice ofspinner shape, bearing in mind that it is always a surface of revolutionabout a spin axis, is mainly guided by practical manufacturingconsiderations after first satisfying the requirement for shapes thatyield laminar flow conditions when used in accordance with theprinciples of the invention. The various design parameters of thefiltration unit according to the present invention are discussed belowin conjunction with FIGS. 15 through 26.

One of the most basic issues which must be addressed was alluded toearlier when it was stated that Uc increases monotonically with S.Residual cell concentration cannot be computed without first knowing therate at which plasma is removed, and this requires a more specificstatement of the relationships between U_(c) and S. The question of howto relate plasma flux to shear rate is best answered by the work ofBlackshear and Forstrom and, as amended by Porter and Lopez.

The former authors made use of a couette membrane filter configurationin which the outer wall rotated and the inner cylindrical membrane wasstationary. They tested a variety of RBC suspensions including wholeblood, human and animal, and hematocrits from near zero to about 40%.Their data clearly show a transition from the condition ofnon-polarization wherein RBC do not enter pores, noted by a lack ofhemolysis, to polarization where they do enter the pores as signified bya sudden onset of hemolysis. A critical TMP at which this occurs wasdescribed by Zydney and Colton who derived an expression for thedependence of plasma flux upon shear rate based upon the existence ofthe concentrated polarization layer and enhanced diffusion from thatlayer. However, it is the purpose of the applicant's invention torestrict operation of the device to the condition of depolarization asnoted above. For this purpose Blackshear and Forstrom's definition of acritical filtration velocity, U_(c) is more useful. It is quiteliterally the mean velocity of permeate through the membrane as averagedover an element of membrane area. It is not the actual velocity ofpermeate in a pore.

Blackshear and Forstrom first defined the critical filtration velocityas that value at which filtration drag is just balanced by repulsiveforces at the membrane surface. Any greater filtration velocity willdrive the RBC onto the membrane or into the pore. While it is difficultto compute the absolute magnitude of these several forces withprecision, their dependence upon the controlling parameters can bededuced and a ratio formed between opposing forces. The ratio constantcan then be measured experimentally as well as the predictive accuracyof the functional relationship of parameters.

Blackshear's and Forstrom's analysis can be identified in greater detailin the extant scientific literature, whereas their results are givenhere only summarily. In brief, U_(c) was found to be proportional toS¹.5 and a parameter they defined as λ⁻¹ which latter value depends onlyupon the local hematocrit, i.e., fractional cell volume of the bloodbeing filtered. The proportionality also depends upon cell radius andsuspending medium or plasma kinetic viscosity, but these are not designparameters to be determined. However, because the Blackshear/Forstromexperiments were conducted with a stationary cylindrical membrane and aspinning outer wall, the blood flow profile was limited to undisturbedcouette shear of concentric laminar sheets of fluid. Given thesecircumstances, the actual shearing rate at the membrane surface is verynearly the nominal mean value given by spinner surface speed divided bygap thickness. On the other hand, when the inner surface, i.e.,membrane, is spun, the blood flow profile is generally of the Taylorvortex type wherein the shearing rate within the laminar boundary layeris enhanced, see Lopez, by the action of the induced secondary flow. Inthis instance, the relationship must be modified to:

    U.sub.c ∝λ.sup.-1 S.sup.x

In accordance with Lopez, x can have a value of 1.5 to somewhat inexcess of 2.0. The actual value is best determined experimentally as itis very difficult to predict reliably on purely theoretical grounds. Itis believed that the best value for normal blood in accordance with thepresent invention is x=1.625.

Another modification of the Blackshear/Forstrom formula is necessarybecause their expression for λ is accurate only at low to moderatehematocrits which covers the range actually tested by Blackshear, i.e.,0 to 0.4. If the present invention is utilized for plasma collection ina typical clinical setting, blood enters at a hematocrit of about 0.4 to0.45 and leaves at 0.8 to 0.9, or well above the range tested byBlackshear. For his purposes, Blackshear used a formula derived by Tambased upon a stochastic analysis of point forces at the centers ofspherical particles. The results are seen to be representative at lowconcentrations, but the formula predicts an infinite force for H 2/3. Ifspheres are packed together as close as possible without distortion,they can only occupy 74% of the available volume. Fluid flows throughsuch a matrix without infinite resistance. It is clear that the modelbreaks down for H well below 0.67 whereas RBC can pack together soclosely as to take up 97% of the available volume, Chien.

A more appropriate model for high hematocrit is given by Kays andLondon, where the cloud of RBCs is treated as a stationary matrix ofsurfaces past which fluid must flow in order to traverse the membranewhile leaving the cells behind, in effect, convective drag.

A quantitative comparison of the two models is shown in FIG. 15 which isa plot of λ⁻¹, that is, the reciprocal of the Blackshear and Kaysparameters, respectively. It is seen that both expressions yieldapproximately the same values for H between about 0.2 and 0.4. Above 0.4the Kays model prevails, justified only by the fact that this modeldoes, indeed, correlate with observed empirical results. The importanceof the λ⁻¹ function is quite apparent due to the profound effect it hason lowering the value of U_(c) for increasing values of cellconcentration. A reasonably accurate model is imperative, and, it isnoted that in either model the parameter λ⁻¹ depends only uponhematocrit, H.

Given the now-established relationship between "critical" or, in effect,maximum filtration velocity, U_(c) and the parameters shear, S andhematocrit, H through the λ⁻¹ function, it is useful to also state therelationship between blood viscosity, μ, and hematocrit, H, so that theexpression for shear stress, namely, τ=μS, can be cast in the sameparametric terms. The data published by Rand for high values of shearrate serves this purpose and can be summarized as follows: ##EQU1## aand b are constants which depend somewhat upon blood temperature, whichdependency is ignored to keep the example as simple as possible. Thestated values are for normal blood temperature of 37° C.

The critical filtration velocity model, together with the aboveexpression for blood viscosity and the design criteria given,hereinabove, can now be combined with continuity expressions to yieldthe fundamental design equation, namely: ##EQU2## x is position alongthe spin axis as measured from the beginning of the active filteringportion of the membrane near the blood entrance. See FIG. 17. Thegeometry of the device is inherent in this equation through theimposition of a constant or only slightly varying Taylor number. Thismathematical condition assures that laminar flow can be maintainedthroughout the device. The only remaining unspecified geometricalparameter, namely, D_(x) ' is the local slope of the spinner surfacerelative to the spin axis at position, x. Subscripts 1 and 2 willhereinafter refer to entrance and exit values, respectively. Theproportionality constant has physical meaning in terms of a rigorousmathematical derivation, but, for the sake of brevity, it is sufficientto say that k can be evaluated by setting the upper limits of the left-and right-hand integrals at H₂ and L, the spinner length, respectively.The ratio of the two integrals thus evaluated at their definable limitsyields k.

The more important point to be made is that the left-hand integral is ananalytic function in terms of the single parameter, H. The right-handintegral can be evaluated by numerical computer methods, again, in termsof the single parameter, x. It is literally the axial arc length of thespinner surface profile taken in section containing the spin axis. Thus,hematocrit, H is completely defined as a unique function of position, x,wherein it is only necessary to specify entering and exitinghematocrits, total rotor arc, or axial length, which are nearly thesame, and an initial slope, D_(x) ' for the spinner at the bloodentrance. This hematocrit function further defines the variation ofviscosity with position by virtue of the relationship between μ and Hgiven above and, in turn, the inverse variation of shear rate, S with μwhich must be designed into the gap geometry. That is, S=τ_(M/)μ whereτ_(M) denotes the maximum permissible shear stress va for blood, namely,1500 dynes/cm.² or some lower value. As so much depends upon being ableto specify the hematocrit function, H(x), it is plotted in FIG. 21 as afunction of the normalized position parameter, X=x/L. Because theslopes, D_(x) ' in most practical designs are comparatively shallow, andthe denominator in the arc length integral is a cosine function, thereis very little effect upon the function H(X) for a wide variety ofdesign shapes, specifically, rotor shapes. The curves in FIG. 21 are,therefore, substantially representative of most practical shapeconfigurations, even if those shapes are varied over many potentiallyuseful options, provided the stated principles of the invention aremaintained. The curves are plotted for several values of a plasmaextraction fraction, f, defined as the fraction of available incomingplasma that is actually removed by filtration. The fraction, (1-f) iswhat is left to carry the concentrated RBC out of the device. Theinitial hematocrit, H₁ was selected to be a general population meanvalue of 0.45.

Another result that follows immediately from the principles of theinvention, as represented in the fundamental design equation, withoutfurther regard for specific geometry, is the critical filtrationvelocity, U_(c) (x) as a function of position along the activelyfiltering portion of the membrane. This result derives from havingspecified H,μ, and S all as a function of position, x. One then uses thecritical filtration velocity model referred to above to compute U_(c)(x). It is one object of the invention to cause the actual plasmapermeation rate to be equal to U_(c) (x) everywhere on the membrane bydesign of the membrane substrate and permeate flow paths. The normalizedfunction, U_(c) (X) is essential for this purpose and is plotted in FIG.26, again, for several values of f. The values of U_(c) shown on theordinate scale are in units of cm./sec. and represent actual plasmafiltration rates obtainable from whole blood under a constant shearstress of 1500 dynes/cm.². The entering hematocrit is again taken to be0.45. A striking feature of these curves is their precipitous drop verynear the blood entry point. This may be interpreted to mean that most ofthe plasma is removed very quickly before the blood becomes too thick.Much of the remaining portion of the device serves largely to milk theremaining concentrated RBC suspension in order to achieve the specifiedend point plasma removal fraction, especially if that is an aggressivefraction. This characteristic can be attributed to the nature of the λ⁻¹function shown earlier in FIG. 15. Simply stated, as blood thickens withcells, it very quickly becomes increasingly more difficult to extractplasma.

Given the distribution of plasma flux, it is possible to integrate overthe membrane area to obtain the overall performance of the device whichcan be stated in terms of general operating parameters. It is convenientto define the total plasma flux rate, P in relation to the incomingblood flow rate, V_(Bl). In effect,

    P=(1-H.sub.1) f V.sub.B1

where H₁ and f are as defined above. The outlet hematocrit, H₂ isuniquely related to f given the initial hematocrit, H₁. ##EQU3##

A mean filtration velocity, U for the device as a whole may be writtenas:

    U=P/A.sub.M

where A_(M) is the active membrane area. U is the principal figure ofmerit for the device. Given U, one can scale the membrane area to obtainany desired total plasma flux rate, P=UA_(M) ; provided, of course, thatV_(B1) is great enough to supply the plasma.

Not unexpectedly, we find that, as one attempts to extract higherfractions of plasma, the figure of merit diminishes, whereas it ishigher for larger values of maximum operating shear stress. This isshown in FIG. 19 which plots U vs. f for several values of τ_(M). If onetakes only half the incoming plasma, it is possible to get 6 cm./min.,i.e., 6 ml. per minute of plasma per cm.² of membrane at a shear stressof 1500 dynes/cm.². At 80% plasma extraction, this value drops to about1.6 cm/min. Compared to other methods of membrane filtration of plasma,this is still an extraordinarily high value.

It is particularly instructive to compare the figure of merit inaccordance with the invention with that obtained using the Lopez couettemembrane configuration. The latter describes an essentially constantshear rate, whereas the instant invention describes a constant shearstress. In the interest of a strict comparison, the Lopez configurationwill be allowed the optimum benefit of operating everywhere at thecritical filtration velocity, although Lopez never actually addressedthe issue of varying conditions within his device. It is still theclosest approximation of the instant invention in the extant literature.Although not explicitly presented here, the fundamental design integralequation for the Lopez configuration is somewhat different from thatpresented hereinabove in accordance with the principles of the instantinvention. However, the same mathematical technique is applicable andyields the required specification of H, μ, and U_(c). S, of course, isconstant. Integration of U_(c) yields a value of U, and we form theratio: ##EQU4## The result of this calculation depends only upon f,given H₁, and is plotted in FIG. 20 for H₁ =0.45. Clearly, thefiltration efficiency that can be achieved with constant shear stress isgreater than that achieved with constant shear rate. The degree ofimprovement does not depend upon either the shear stress or shear ratevalues that are utilized. Initially, at f=0, there is no improvementbecause there is no change in viscosity from entrance to exit. As fincreases to 0.73, the improvement ratio rises at a slightly increasingrate to about 1.54 or a 54% greater filtration rate in the device aspracticed in accordance with the invention over that of Lopez. Thislevel of improvement holds to a value of f=0.81. At higher values of f,the ratio falls off until it is again null at f=1.0. The latter effectis due to the fact that, when one attempts to take all of the incomingplasma, i.e., f=1.0, then both devices approach zero efficiency ofoperation; that is, both require an infinite amount of membrane. Thisinteresting result shows that there is an optimum degree of improvement,and that it occurs when one withdraws approximately 77±4% of theincoming plasma. The maximal improvement over Lopez should be regardedas significant, because it not only reduces the size and probable costof the device by 35%, but the effect upon blood damage is similarlyreduced, as will be described immediately below.

So long as plasma flux is never driven beyond the critical filtrationvelocity for either the instant invention or the device designedaccording to Lopez, the two may be compared as to their effect on RBCdamage, i.e., hemolysis. The primary source for hemolysis under thiscondition is occasional interaction of the cells with the membranesurface, even if cells do not remain on, or pass through, the membrane.Sutera described this process in quantitative terms by measuring therate at which hemoglobin is lost by RBCs subjected to shearing in acouette viscometer. Again, it was found that hemoglobin loss wasuniquely related to shear stress, not shear rate. When the wallinteraction parameter of Sutera is transformed in terms of the analysisherein and integrated over the total quantity of processed blood, it ispossible to derive a value for the concentration of free, i.e., unboundhemoglobin contained in the residual plasma which remains to carry theconcentrated RBCs This value, designated Hb_(r) is proportional to τ3/8M, that is, the shear stress raised to the power 3/8. Theproportionality coefficient is a function of f and H₂ only, except thatit is higher in the Lopez configuration by the magnitude of the ratio ofU for the instant invention to U for Lopez plotted earlier in FIG. 20,also as a function of f. Consequently, if one removes about 80% of theincoming plasma, the residual plasma in the Lopez device will have a 54%higher concentration of free hemoglobin than would be present in theresidual plasma of a device in accordance with the invention.

However, what really counts in a clinical setting is how the plasma freehemoglobin of the donor is affected after donation is completed. Thecriterion for clinical acceptability of any design requires that theplasma donor not be adversely affected. In order to assess this effect,we may write the percent increment, % ΔHb of free hemoglobin found inthe plasma of a normal donor as: ##EQU5## where Hb_(n) is theconcentration of free hemoglobin in normal plasma, and P_(b) is thetotal body volume of plasma, both quantities being measured in thenormal donor prior to donation. P_(p) is the total amount of plasmacollected from that donor. The plasma-free hemoglobin concentration inthe donor after donation, Hb_(D) is: ##EQU6## A typical range of valuesfor Hb_(n) in the normal adult population is 2 to 3×10⁻⁵ gm./ml Atypical value for P_(b) is 3.0 liters and P_(p) for that size adult is600 ml. or about 20% of the donor's pre-donation plasma volume.

Using the above expressions and a starting value of Hb_(n) in themid-range, or 2.5×10⁻⁵ gm./ml., FIG. 16 shows how % ΔHb and Hb_(D) varywith applied shear stress, τ_(M). The curves presuppose constant shearstress throughout the gap which, indeed, describes the device whendesigned in accordance with the instant invention. The assumption is notvalid if the Lopez configuration is used without alteration. Thecomparisons are, nevertheless, instructive. The upper curve representshow the unmodified Lopez configuration would be expected to performunder the conditions cited above. It is seen that, starting from amedian value of 2.5×10⁻⁵ gm./ml., the physiological upper normal valueof 3.0×10⁻⁵ gm./ml. is reached before the Nevaril limit of 1,500dynes/cm.² can be usefully applied. This is an arbitrary limit; onemight say that 4.0×10⁻⁵ gm/ml. is not an unreasonable plasma freehemoglobin level which the healthy donor would quickly clear from hissystem. But, this is not equivalent to saying the frequent, repeating,plasma donor is clinically unaffected. On the other hand, if theimproved efficiency of the instant invention is utilized, one may expectthe performance of the lower curve, wherein, the donor plasma hemoglobinincreases from the median level to what might be a more acceptable upperlevel, i.e., a 32% increase, only after the Nevaril critical limit ofshear stress if first reached. In either case, one must be in a positionto say that the donor is clinically unaffected or medicallyuncompromised for all practical purposes. It is noted that there is noproven medical basis for any of these arbitrary plasma hemoglobin limitsbut, in the absence of confirmed long range clinical evaluation, one iscompelled to adopt the most conservative possible judgment, particularlyif the health of a frequent and persistent donor is in question. In anycase, it is clear that the instant invention allows one to operate atmuch higher shear stress levels and, therefore, much higher filtrationefficiency for any given hemolysis limit.

The final step in the analysis deals with a specific determination ofgeometrical parameters. While the shape of the spinner, that is, itsdiameter, D(X) as a function of normalized position, X=x/L is somewhatarbitrary, within the limits of laminar flow, once D(X) is specified,the gap thickness, d(X) is rigorously determined. The most generalstatement which describes the behavior of the function, d(X) (X is, byconvention, always measured from the point of blood entry) is: ##EQU7##The first factor on the right-hand side is a proportionality constantincluding the constant, a, defined earlier above, the blood density,ρ_(B), and the spin rate, Ω in radians per second. All units are in cm.,gm., and seconds, unless otherwise specified. The second factor, Ta isthe Taylor number which has been allowed to vary, to a limited extent,with position, X. The third factor depends upon spinner shape, and thefourth factor makes use of the function, H(X) previously determinedabove. It is this latter factor which has the most powerful effect onthe change of d with X. In effect, because H always increasesmonotonically with X, the exponential function tends to dominate overany reasonable change in Ta or D so that d generally increasesmonotonically with X as well.

The issue of laminar flow is unequivocally settled by the magnitude ofthe Taylor number, given the inner spinning member and stationarycontainment vessel of the instant invention. A preferred, but notessential, range of operation would be for Taylor numbers in excess of40, where laminar Taylor vortices obtain and serve to enhance theshearing effect at the membrane surface. On the other hand, much largerTaylor numbers are not preferred, as these tend toward generalturbulence. One way to assure that the latter condition does not occuris to require that the Taylor number does not vary significantly as afunction of position, X.

In fact, if the Taylor number is held rigorously constant, then both thegap thickness, d(X) and the spinner diameter, D(X) are uniquelydetermined as follows: ##EQU8## The numerical subscripts again indicateentering or exiting values. The first factor on the right-hand side, insquare brackets, is a constant coefficient. The shapes are controlled bythe exponential functions, and it is obvious that D(X) gets smaller withincreasing X, while the gap, d(X) gets bigger. These curves are plottedin FIGS. 22A and 22B on an exaggerated scale so that the relativeprofiles can be more easily appreciated. What is actually plotted arethe quantities: ##EQU9## In this way, all the dimensional quantities arenormalized relative to the initial spinner diameter, D₁, and only thecurvatures are shown, these being relative to an axis which intersectsthe terminal diameter, D₂ and is parallel to the pin axis. See FIG. 17.This graphical convention allows one to depict subtle curvatures andvery narrow spacings on an expanded scale. It should be understood thatthe exaggerated curvatures of FIGS. 22A and 22B are of schematicsignificance only, and that the geometry, when drawn in uniformproportions, is characterized by slight curvatures approximatingtruncated cones and close spacing. It is noted that the curvatures ofFIGS. 22A and 22B, shown for f=0.8 and 0.9, respectively, are easilyscaled to any size device upon selection of D₁, d₁, H₁ and L. Selectingf uniquely establishes the function, H(H).

The selection of d₁, D₁, and L should not be arbitrary. It is guided bythe fact that the spin rate, Ω is uniquely related to the ratio, d₁ /D₁in accordance with the curves shown in FIG. 18, where Ω is plotted inunits of R.P.M. for several values of shear stress, ρ_(M). For example,if d₁ /D₁ is 0.01 (i.e. a 0.011" gap for a 1.1" initial diameterspinner), the spin rate for 1500 dynes/cm.² of stress is 6100 R.P.M. Ifone prefers a larger gap, it is seen that a 0.022" gap requires 12,200R.P.M. for maximum usable shear stress, i.e., maximum efficiency.Clearly, one wants the narrowest practical gap.

Also plotted in FIG. 18 is the Taylor number, Ta as a function of theactual initial gap dimension, d¹. Using the same two examples above, a0.011" gap corresponds to a Taylor number of 76, while the 0.022" gapoperates at a Taylor number of 420. The narrower gap is clearly withinthe laminar Taylor vortex range. The larger gap is not so certain.

As a practical matter, the curvatures shown in FIGS. 22A and 22B,although exaggerated, clearly suggest, on the one hand, the difficultythat one would experience in trying to mount flat sheet membranes on adoubly-curved spinner while, on the other hand, when viewed in truescale, the close approximation of the spinner to a frustum of a righttruncated circular cone. Recalling that, in any case, the spinner shapeis somewhat arbitrary, one would be well advised to relax the conditionof a rigorously constant Taylor number and opt for a spinner having astraight-sided profile when viewed in axial section, i.e., a truncatedcone. One could select an apical angle that most closely approximatesthe spinner of FIG. 22A, 22B. The gap spacing is essentially unaffectedif measured relative to the new spinner profile. A more rigorousapproach, which is offered herein as the most preferred embodiment ofthe instant invention, selects an apical angle which minimizes the rootmean square variation of Taylor number as averaged over the activemembrane surface. This approach, for all practical purposes, maintainsadequate control over the Taylor number while permitting the neededflexibility to choose a more easily fabricated spinner design. Theresults of these rather complex calculations can be summarized asfollows: ##EQU10## The first expression is simply a cone extending fromX=0 to X=1.0. The second expression is the increasing spacing relativeto that cone. The parameter, h will be specified momentarily. h/2represents the slope of the sides of the cone relative to the spin axis.A plot of these surfaces, shown in axial cross section, and in a mannerentirely analogous to the curves of FIGS. 22A and 22B, are presented inFIGS. 24A and 24B, again, for f=0.8 and 0.9, respectively. As specified,the spinner is straight sided, that is, curved only about its spin axis,while the containment vessel has an interior profile which is convexoutward. In the previous example, the profile is concave outward. Theinitial boundary values, d₁ /D₁ and d₁ are selected as previouslydescribed using the curves in FIG. 18. This will yield an initialboundary value for the Taylor number Ta₁. In this example, however,Ta(X) is not invariant, but can be calculated as shown in the curves ofFIG. 25. The plot is of Ta(X)/Ta.sub. 1, that is, the normalizedvariation. One can note that the variation reaches a peak and thensubsides, indicating quite adequate restriction of the Taylor numbervariance. For example, for f=0.8, the Taylor number increases, at itsmaximum excursion, by only 25% over its initial value at X=0. In theexample used previously, if d₁ is taken to be 0.011" and D₁ to be 1.1",the Taylor number would go from 76 to somewhat less than 100 at itsmaximum excursion. This is a range which assures laminar flow within theshear gap.

In order to complete the geometrical specification, the value of h isdetermined as follows: ##EQU11## This expression must be solved for hafter first specifying the initial diameter, D₁ and the requiredmembrane area, A_(M). As previously explained, A_(M) is scaled inaccordance with the device effectiveness, U where A_(M) =P/U or, theratio of total plasma collection rate in ml./min. to the figure of meritin cm./min. The parameter, Q derives from minimizing the variance ofTaylor number and is plotted in FIG. 23 as a function of f for severalvalues of initial hematocrit, H₁. Using the typical average of 0.45hematocrit and an operating plasma extraction fraction of 0.8, Q has avalue of about 0.305.

The foregoing analysis has been based upon the premise that the criticalfiltration velocity, U_(c) (X) plotted in FIG. 26 obtains at all pointsalong the membrane. When plasma is initially drawn through the membranethis condition may or may not be satisfied, depending upon the design ofthe underlying membrane support in relation to the dynamics of plasmaflow. Nevertheless, when steady state is reached and maintained thestated condition automatically prevails. This is due to the fact thatfiltration of suspensions is a self-limiting process, see Porter.Initially, given that TMP does not vary significantly over the membranesurface, the flux velocity is essentially uniform before the variationof hematocrit is impressed upon the axial distribution of RBC. As theconcentration of cells increases near the outlet, the filtration fluxvelocity at that point is too high to prevent concentration polarizationso that cells impinge the membrane and begin to plug the pores to somedegree. This causes increased membrane resistance and retards the flowof permeate. If the total mean filtrate flux, U is controlled by othermeans, in other words, held invariant, the drop in actual flux velocity,U near the exit must force an increase in that velocity near theentrance where it was initially well below the critical value, U_(c)described hereinabove for given conditions of shear and hematocrit. Solong as U, at any point along the membrane continues to exceed thecritical value, U_(c) for that point, the membrane will continue to plugand form a concentrated polarization layer, and U must continue to fall,ultimately to the value, U_(c), which is the highest value U can havewithout further increasing net effective trans-membrane resistance. If Uis restricted to that specified hereinabove for the stated conditions,then U will rise from its initial value near the entrance of the deviceto the critical value U_(c), while U will fall from its initial valuenear the exit of the device to the critical value, U_(c) for thoseconditions. The flux velocity distribution, such as that shown in FIG.26 represents the final equilibrium condition achieved, in part, by theformation of an increasing degree of concentration polarization towardthe blood exit of the device.

In such circumstances the sensible TMP across the membrane is stillvirtually uniform but, in those sections where concentrationpolarization exists to some degree, a portion of the TMP is used upacross the concentrated layer of cells. Hence, the effective TMP is lessthan the observed value which accounts for most of the decrease in U.Only when U is less than, or equal to, U_(c) does the concentrated celllayer cease increasing. Nevertheless, it is physically possible toincrease the impressed TMP so that U is greater than the value specifiedherein as being the correct limit in accordance with the principles ofthe instant invention. This compels polarization of the entire membrane,defeats the type of operation and method described herein and becomes asystem in which the membrane operates more in accordance with thatdescribed by Solomon, Castino, or Zydney.

In order to avoid even the initial polarization of a portion of themembrane it is possible to impose a permeate

flux velocity distribution, U_(c) (X), such as that illustrated in FIG.26, by artificially creating a variation in TMP. It is in the nature ofthe device concept, as first used by Lopez and subsequently improved inthe invention herein described, that the resistance to flow of the feedsolution, blood in the present case, across the entire device, isinherently low. Consequently, the static pressure on the blood side doesnot vary significantly from entrance to exit. However, resistance topermeate flow can be increased within the membrane support structure.Any number of mechanical means can be devised to effect this result.Some examples are, (1) narrowing the channels 17 underlying the membrane18 (see FIGS. 2 and 9) so that more of the membrane is masked by itssupport structure while the outflowing permeate (e.g., plasma)experiences greater flow resistance, or (2) support the membrane with agraded filter having tighter porosity in those portions where a lowerflux velocity is desired. In example 1, the plasma outflow channelsunderling the membrane are narrowest near the blood exit and plasma mustflow the entire length of the channel back toward the top of the device,joining additional plasma along the route before it is all collected incircumferential collection channel 89 as shown in FIGS. 1, 2, and 9.Thus, the lowest membrane support resistance is near the blood entrancewhile the highest such resistance is near the blood exit.

Accordingly, it is one object of the present invention to vary theresistance to plasma flow within the membrane support structure so thatthe natural local plasma flux velocity, U is everywhere just slightlybelow the critical flux velocity, U_(c), described hereinabove for theconditions existing at all points along the membrane, provided furtherthat U, also defined hereinabove is, itself, not exceeded. Given thiscondition, concentration polarization of RBC will not occur anywherealong the membrane.

In the foregoing specification, reference has been made at variouspoints to the separation of plasma from whole blood and the "collectionof red blood cells." In all such references, the term "red blood cells"is intended to mean and does mean the collection of all corpuscularmatter suspended in the blood and is not restricted merely to red bloodcells alone.

What is claimed is:
 1. An apparatus for filtering a fluid suspensioncontaining particles of living matter origin capable of being damaged ifsubjected to shear stress above a predetermined level, comprisinga firstsurface of revolution, a membrane comprising a second surface ofrevolution coaxial with and spaced form he first surface said first andsecond surface forming a means for defining a shear gap of predeterminedradial dimensions between the surfaces, said dimensions increasing alongaxial lengths of said surfaces, inlet means for introducing the fluidsuspension into the gap, means for rotating one of said surfaces aboutits axis of revolution relative to the other surface at an angularvelocity such that shear stress below said level is imposed on the fluidsuspension in the gap, whereby fluid is separated from the fluidsuspension and passes through pores define by the membrane, first outletmeans for collecting fluid passing through the membrane, and otheroutlet means for removing fluid form the gap remotely from said inletmeans, the viscosity of the fluid remaining in the gap increasing in adirection toward said other outlet means, and said means defining saidshear gap to have gap radial dimensions between said first and saidsecond surfaces increasing in said direction toward the other outletmeans in such relation to aid viscosity increase in said direction thatthe shear stress in the fluid suspension at and along the membranesurface is maintained substantially constant.
 2. An apparatus accordingto claim 1 wherein the fluid suspension is whole blood.
 3. An apparatusaccording to claim 2 including means for controlling the speed ofrotation such that the shear stress is raised to and maintained at apredetermined level immediately below the shear stress at whichsignificant hemolysis begins.
 4. The apparatus according to claim 3where the first surface and membrane surface have elongated curvilinearprofiles of a predetermined relation to each other.
 5. An apparatusaccording to claim 3 wherein the membrane surface is rotatable and thegap dimensions are selected at predetermined minimum values and whereinthe means for controlling speed of rotation is adjusted such that shearstress is maintained below the predetermined maximum value.
 6. Anapparatus according to claim 5 wherein the level of shear stress ismaintained at less than 1500 dynes/cm².
 7. An apparatus according toclaim 1 wherein the first surface and membrane surface are conicallytapered.
 8. An apparatus according to claim 1 wherein the first surfaceis stationary and the membrane surface is rotatable.
 9. An apparatusaccording to claim 1 wherein the first surface is rotatable and themembrane surface is stationary.
 10. An apparatus according to claim 1wherein the gap dimension, angular velocity, transmembrane pressure andflow rate of the fluid suspension are maintained at values such that therate of withdrawal of the fluid from the fluid suspension does notexceed the critical filtration velocity for the fluid suspensionanywhere on the surface of the membrane.
 11. An apparatus according toclaim 10 including elongated membrane support means extending along thesecond surface of revolution parallel to the axis of revolution.
 12. Anapparatus according to claim 11 wherein the membrane support meansincludes means for varying the resistance of the membrane support meansto the flow of fluid passed through the membrane.
 13. An apparatus asdefined in claim 1 wherein the ratio of the gap radial dimensionsbetween said surfaces, as measured proximate axially opposite ends ofthe gap, is at least about 1.65.
 14. An apparatus for filtering plasmafrom whole blood comprisingan elongated housing having an interiorsurface of revolution of a first predetermined profile which is taperedaxially of said interior surface, an elongated membrane filter havingpores and an exterior surface of revolution of a second predeterminedprofile which is tapered axially of said exterior surface and rotatablydisposed within the housing, said interior and exterior surfaces forminga means for defining a narrow annular gap between the interior surfaceof the housing and the exterior surface of the membrane filter, saidexterior and interior surfaces being coaxial, and means for rotating themembrane filter about its axis of revolution at an angular velocity suchthat at any location on the membrane near a pore or pores the product ofthe filter angular velocity and radius at said location, divided by thelocal gap thickness, has predetermined relation to local bloodviscosity, said angular velocity being below that at which significantdamage to re blood cells is encountered, whereby plasma is separatedfrom the whole blood introduced into the gap and passes through themembrane, there being inlet means to pass whole blood into the gap,first outlet means for collecting plasma passing through the membrane,and other outlet means remote from said inlet means to remove from thegap blood from which plasma has been removed via the membrane, saidlocal blood viscosity in the gap increasing in a direction toward saidother outlet means, said means defining said gap to have gap radialdimensions between said exterior and interior surfaces increasing insaid direction toward the other outlet means in such relation to saidviscosity increase in said direction that the shear stress in the bloodin the gap at and along the membrane surface is maintained substantiallyconstant.
 15. An apparatus according to claim 14 wherein the thicknessof the gap increases in the direction of elongation.
 16. An apparatusaccording to claim 15 wherein said inlet means is located at the end ofthe apparatus adjacent the narrowest gap dimension, said first outletmeans is located at the end of the apparatus adjacent the widest gapdimension, and said outlet means for plasma is located at the end of theapparatus adjacent the inlet means, the membrane filter exterior surfacedecreasing in diameter in an axial direction form the inlet means towardthe outlet means.
 17. An apparatus according to claim 16 wherein saidfilter includes a spinner and the angular velocity of the filter ismaintained at a value such that the flow of blood in the gap is laminar.18. An apparatus according to claim 17 wherein said spinner mounts themembrane and the gap dimension, angular velocity, transmembrane pressureand flow rate of whole blood are maintained at values such that the rateof withdrawal of the plasma does not exceed the critical filtrationvelocity for blood anywhere on the surface of the membrane filter. 19.An apparatus according to claim 18 wherein the membrane filter includesmembrane support means for receiving plasma passing through the membraneand communicating the plasma longitudinally to a central collectionpoint.
 20. An apparatus according to claim 19 wherein the membranesupport means includes means for varying the resistance of the membranesupport means in a predetermined manner to the flow of plasma passedthrough the membrane.
 21. An apparatus according to claim 20 wherein theprofiles of the interior surface and filter are conical.
 22. Anapparatus according to claim 17 wherein the dimension and geometry ofthe gap, the flow rates and the angular velocity of the apparatus arevaried in a predetermined manner such that the Taylor number for thefluid suspension is maintained essentially constant over the entirelongitudinal length of the membrane filter.
 23. An apparatus accordingto claim 22 wherein the profile of the filter is defined by an invertedtruncated right circular cone and wherein the apical angle of the coneis selected such that minimum variation of the Taylor number over theentire longitudinal extent of the membrane is produced.
 24. An apparatusaccording to claim 17 wherein the angular velocity is selected such thatthe Taylor number for the blood in the gap does not exceed 1000, and thespinner carries the membrane.
 25. An apparatus as defined in claim 14wherein the ratio of the gap radial dimensions between said surfaces, asmeasured proximate axially opposite ends of the gap, is at least about1.65.
 26. An apparatus for filtering fluid suspensions comprising:anelongated hollow container having an interior wall with a firstpredetermined tapering profile; an elongated core element disposedwithin the container having a second predetermined tapering profile,said profiles forming a means for defining a gap having a thicknesswhich varies in the direction of elongation in a pre-determined mannerbetween the interior wall and the core element; said interior wall ansaid core element being co-axial, inlet means locate at one end of theapparatus; means for introducing a fluid suspension through the inletmeans into the gap; means for rotating the core element about its axisof rotation at a predetermined angular velocity within the containersuch that, due to the geometry and configuration of the gap, essentiallyuniform shear stress is imposed on the fluid suspension over the entiresurface extent of the core element; first outlet means located at theinlet end of the apparatus for removing fluid extracted from the fluidsuspension; second outlet means located at the end of the apparatusopposite the inlet end for removing the remaining portion of the fluidsuspension; membrane means disposed over the exterior surface of thecore element for filtering and separating the fluid from the fluidsuspension when the core element is rotated, the membrane having anexterior surface; and means for communicating the filtered fluid fromthe side of the membrane opposite the fluid suspension to the firstoutlet means, the viscosity of the fluid suspension in the gapincreasing in a direction toward said second outlet means, and saidmeans defining said gap to have gap radial dimensions between saidinterior wall and the exterior surface of the membrane increasing insaid direction toward the second outlet means in such relation to saidviscosity increase in said direction that the shear stress in the fluidsuspension at and along the membrane surface is maintained substantiallyconstant.
 27. An apparatus according to claim 26 wherein the gap isnarrower at the inlet end of the apparatus and wider at the outlet end.28. An apparatus according to claim 27 wherein the profiles of theinterior wall and core element are conical.
 29. An apparatus accordingto claim 28 wherein the apparatus is vertically oriented and the fluidsuspension in the gap flows from the inlet means to said second outletmeans under the influence of differential pressure and gravity.
 30. Anapparatus according to claim 29 wherein the fluid suspension is wholeblood, the fluid extracted from the suspension via membrane pores isplasma, and the remaining portion of the fluid contains concentrated redblood cells and other blood particulate matter.
 31. An apparatusaccording to claim 30 wherein the shear stress to which the blood issubjected is maintained below the value at which significant damage tothe red blood cells occur.
 32. An apparatus according to claim 31wherein the angular velocity of the core element is selected at a valuesuch that the flow of blood in the gap is laminar in the Taylor vortexsense.
 33. A apparatus according to claim 32 wherein the dimensions andgeometrics and operating parameters are varied in a predetermined mannersuch that the Taylor number for the fluid suspension is maintainedessentially constant over the entire longitudinal length of the coreelement.
 34. An apparatus according to claim 32 wherein the angularvelocity is selected such that the Taylor number for the blood in thegap does not exceed
 1000. 35. An apparatus according to claim 31 whereingap dimensions are selected at predetermined minimum values and theangular velocity of the core element is controlled such that the bloodis subjected to shear stress slightly less than the shear stress atwhich significant hemolysis begins to occur.
 36. An apparatus accordingto claim 35 wherein the shear stress to which the blood is subjecteddoes not exceed 1500 dynes/cm².
 37. An apparatus according to claim 26wherein the core element includes a plurality of ribs and channelshaving a tapering width and depth extending longitudinally along theexterior surface of the core element.
 38. An apparatus according toclaim 37 wherein the membrane is disposed over the ribs and channels ofthe core element and is secured along each of its longitudinal edges toa selected rib of the core element.
 39. An apparatus according to claim38 wherein a cap is secured to the top of the core element, said capincluding a plurality of radial passages extending through the cap todefine a manifold communicating with the plasma on the fluid side of themembrane and a hollow axial pin axially mounted at the top of the cap.40. An apparatus according to claim 39 wherein a shallow spiral grooveis imparted to the exterior surface of the hollow pin, the spiral grooveextending around the pin in the same direction as the direction ofrotation of the core element whereby the groove exerts a return pumpingaction on plasma exiting from the hollow pin.
 41. An apparatus accordingto claim 40 wherein the core element is hollow.
 42. An apparatusaccording to claim 41 wherein the means for rotating the core elementincludes a magnet disposed in the hollow core element and a source ofmotive power locate externally of the container and magnetically coupledto the interior magnet.
 43. An apparatus according to claim 42 whereinthe core element and magnetic combination has a weight which isneutrally buoyant in blood, whereby the core element floats in wholeblood introduced into the apparatus.
 44. An apparatus according to claim43 where the magnet is a four pole ceramic disk magnet.
 45. An apparatusfor filtering plasma from whole blood comprising:a tapered elongatedhousing having an interior surface of revolution with a firstpredetermined profile; semipermeable membrane means applied to andcovering the interior surface of the housing of the housing; a taperedelongated spinner element having a surface of revolution of a secondpredetermined profile rotatably disposed with the housing, the membranemeans and the surface of the element forming a means defining a narrowgap having radial dimensions varying in a predetermined manner in thedirection of elongation; the membrane means and the surface of theelement being coaxial; means for rotating the spinner element about itsaxis of revolution at an angular velocity and local radius is related tothe uniform ratio of local gap dimension to local blood viscosity andimmediately below the velocity at which significant damage to rd bloodcells is encountered, there being inlet means to pass whole blood intothe gap, and first outlet means remote from said inlet means to removefrom the gap blood from which plasma has been removed via the membrane,the viscosity of the blood in the gap increasing in a direction towardthe outlet means, and said means defining said gap to have gap radialdimensions increasing in said direction toward the outlet means in suchrelation to said viscosity increase in said direction that the shearstress in the blood in the gap at and along the membrane surface ismaintained substantially constant.
 46. An apparatus according to claim45 wherein the thickness of the gap increases in the direction ofelongation.
 47. An apparatus according to claim 46 wherein said inletmeans for whole blood is located at the end of the apparatus adjacentthe narrowest gap dimension, said first outlet means being forconcentrate re blood cells and located at the en of the apparatusadjacent the widest gap dimension, and including second outlet means forplasma located at the end of the apparatus adjacent the inlet means. 48.An apparatus according to claim 47 wherein the angular velocity of thespinner is selected at a value such that the flow of blood in the gap islaminar.
 49. An apparatus according to claim 48 wherein the angularvelocity is selected such that the Taylor number for the blood in thegap does not exceed
 1000. 50. An apparatus for filtering fluidsuspension comprising:a first stationary surface of revolution; a secondsurface of revolution rotatable about its axis of revolution membranemeans covering the stationary surface and having a membrane surface,said membrane surface and said second surface forming a means fordefining a gap of predetermined radial dimensions inlet means forintroducing a fluid suspension into the gap; means for rotating thesecond surface at a predetermined angular velocity such that fluid isseparated from the fluid suspension and passes through the membrane; andfirst outlet means for collecting fluid passing through the membrane;and other outlet means for removing fluid from the gap remotely fromsaid inlet means, the viscosity of the fluid remaining in the gapincreasing in direction toward said other outlet means, the first andsecond surfaces being coaxial, and said means defining said gap to havegap radial dimensions between said first surface and said membranesurface increasing in said direction toward the other outlet means insuch relation to said viscosity increase in said direction that theshear stress in the fluid suspension at an along the membrane surface ismaintained substantially constant.
 51. An apparatus according to clam 50wherein said second surface of revolution is incorporated into arotatable core element and said first stationary surface of revolutionis incorporated into the interior surface of a container for housing therotating core element.
 52. An apparatus according to claim 51 whereinthe fluid suspension comprises a suspension of relatively low densityparticles and the core element is of a weight which is neutrally buoyantin the fluid suspension whereby the core element floats in the fluidsuspension introduced into the apparatus.
 53. An apparatus according toclaim 52 wherein the ratio of specific gravity of the particles to thespecific gravity of the fluid suspension is 3 or lesson.
 54. Anapparatus for filtering a fluid suspension containing particles ofliving matter origin capable of being damaged if subjected to shearstress above a predetermined level, comprising(a) a first surface ofrevolution, (b) a membrane comprising a second surface of revolutionspaced from said first surface, said first surface and said membranesurface forming a means for defining a gap region radially between asurface portion of the membrane and a substantial surface portion of thefirst surface, (c) inlet means for introducing said fluid suspensioninto the gap, first outlet means for collecting fluid passing from thegap through the membrane via pores defined by the membrane, and otheroutlet means for removing fluid from the gap remotely from said inletmeans, (d) means for rotating one of the surfaces relative to the othersurface at an angular velocity such that shear stress is imposed on thefluid suspension in the gap, and the viscosity of the fluid suspensionremaining in the gap increases in a direction toward the other outletmeans, (e) and said means defining said gap to have gap radialdimensions increasing in said direction toward the other outlet means insuch relation to said viscosity increase in said direction that theshear stress at and along said membrane surface is maintainedsubstantially constant and below said predetermined level.
 55. Theapparatus of claim 54 wherein said membrane surface decreases in radiusin a direction toward said other outlet means, such that the Taylornumber for the fluid suspension is maintained substantially constantalong the length of the membrane.
 56. The apparatus of claim 55 whereinthe membrane surface is conical and tapers toward said other outletmeans.
 57. The apparatus of claim 55 wherein the fluid suspensionconsists of blood, and the Taylor number for the blood in the gap doesnot exceed
 1000. 58. The apparatus of claim 54 wherein the fluidsuspension consists of blood.
 59. The apparatus of claim 54 wherein theratio of the gap radial dimensions between said first surface and saidmembrane surface, as measured proximate axially opposite ends of the gapwith the gap radial dimension closer to said other outlet means beingdivided by the gap radial dimension closer to the inlet means, being atleast about 1.65.
 60. The apparatus of claim 54 including support meanscarrying the membrane and rotated relative to said first surface, saidsupport means including means for varying the resistance to flow offluid passing through the membrane such that resistance to such flowincreases at locations corresponding to locations of gap increasingradial dimensions.
 61. The apparatus of claim 54 wherein the membrane isconical and upright, said inlet means and first outlet means are locatedproximate the upper end of the membrane, and the other outlet means islocated proximate the lower end of the membrane.
 62. In apparatus forseparating fluid from a fluid suspension using a couette membrane filterhaving facing coaxial surfaces which together form a means for defininga gap therebetween, there being inlet means for introducing fluid intothe gap, first outlet means for collecting fluid passing through themembrane, and other outlet means for removing fluid from the gapremotely from said inlet means, the combination comprising(a) the filterincluding a membrane having pores to pass the fluid through the membranefrom the gap side of the membrane to the opposite side thereof, (b)means to rotate one of said surfaces coaxially relative to the other,(c) means at said opposite side of the membrane for varying theresistance to flow of fluid passing through the membrane such thatresistance to such flow increases at locations at said opposite side ofthe membrane corresponding to locations of gap increasing radialdimension, (d) and said means defining said gap to have increasing gapradial dimensions being in such relation to increase of fluid viscositydirectionally toward said other outlet means that the shear stress inthe fluid suspension at and along the membrane surface is maintainedsubstantially constant.
 63. The combination of claim 62 wherein saidlast named means includes a membrane support defining flow channels atsaid opposite side of the membrane, the channels having cross sectionsthat decrease in area in said direction.